So, each square on the grid is 10 inches in length and width
To find the dimension of the diagonal lengths, treat them like a hypotenuse so we can use the Pythagorean theorem.
a^2 + b^2 = c ^2
a and b are our length and width and c is the hypotenuse.
Make each diagonal length part of a triangle. There will then be 4 triangles to work with.
Triangle 1 (Top left)
Triangle 2 (Bottom left)
Triangle 3 (Top Right)
Triangle 4 (Bottom Right)
A right triangle made with the top left diagonal dimension will have a vertical dimension of 30 (10+10+10) and a horizontal dimension of 40 (10+10+10+10)
To find c or the hypotenuse, plug these into the Pythagorean theorem.
30^2 + 40^2 = c ^2
c^2 = 900 + 1600 = 2500
c = sqrt(2500) = 50
You will see that triangles 2, 3, and 4 have the same vertical and horizontal dimensions giving them the same value.
Now combine the dimensions
diagonal = 50+50+50+50 = 200
horizontal = 90+90 = 180
diagonal + horizontal = 380
Answer:
k = 3
Step-by-step explanation:
Expanding the first term, we find 1/x at 10(kx)²(1/x)³ = 10k²/x
Expanding the first term, we find 1/x at 8*1⁷(-2/x)¹ = -16/x
Then
10k² - 16 = 74
k = 3
